Md. Aslam Beg Akash

Undergraduate thesis · Mechanical Engineering

Fracture Behavior and Toughness of Ti2N MXene Monolayer under Uniaxial Tension: A Study Using Molecular Dynamics and Fracture Mechanics

Md. Aslam Beg Akash

Khulna University of Engineering & Technology · August 2026

Credits1.5 + 3.0 = 4.5
Obtained gradeA+
SupervisorProfessor Dr. Md. Abdul Wakil · Department of Mechanical Engineering, KUET

The fracture behavior and toughness of monolayer Ti2N MXene were investigated using molecular dynamics. The study examines how fracture strength changes as the initial notch length increases in discrete atomic steps, and evaluates whether fracture mechanics models capture this response.

  • Examined tensile behavior at different temperatures along both orientations.
  • Evaluated fracture strength and toughness using different fracture mechanics models, including linear elastic fracture mechanics (LEFM), nonlinear fracture mechanics (NLFM), and quantized fracture mechanics (QFM).
Pristine Ti2N sheets in the two loading orientations.

Atomic notch construction

Generalized geometric relations were developed to express nominal crack length in terms of the numbers of removed titanium and nitrogen atoms. These relations define the discrete notch-length sequence used to evaluate the fracture response.

Notch construction details and geometry code
Atomic notch geometries and generalized crack-length relations.

Fracture mechanics framework

The nonlinear tensile response of Ti2N MXene was represented using the Ramberg–Osgood relation and incorporated into the fracture analysis. Comparisons with molecular dynamics examine how nonlinear elasticity and an atomic-scale length correction describe the fracture response. [1–3]

Normalized tensile response, fracture-model comparisons and crack opening.
Selected fracture models
Ramberg–Osgood relation: epsilon equals sigma over E times one plus sigma over sigma R raised to m.
The nonlinear energy approximation U e equals two pi a squared B u of sigma, expressed through the constitutive nonlinearity.
Nonlinear implicit fracture relation: pi a sigma f squared times one plus H times sigma f over sigma R raised to m, minus K ref squared, equals zero.
The nonlinear quantized relation replaces a by a plus q over two in the implicit fracture equation.

Fracture resistance in context

Estimated Ti2N fracture resistance and selected literature values. Study conditions differ.

Manuscript in preparation

Nonlinear Elasticity and Fracture Toughness of Monolayer Ti2N MXene

Md. Aslam Beg Akash, Md. Abdul Wakil, Md. Nadeem Azad, Saifuddin Zafar, and Md. Ashraful Islam.

Manuscript writing in progress.

References

  1. [1]I. Greenfeld, S. Jiang, L. Yang and H. D. Wagner. Nonlinear elasticity degrades monolayer fracture toughness. Acta Materialia 286 (2025) 120727.doi: 10.1016/j.actamat.2025.120727
  2. [2]S. Jiang, I. Greenfeld, L. Yang, W. Yin, X. He and H. D. Wagner. Unified fracture criterion for brittle 2D materials. npj Computational Materials 12 (2026) 20.doi: 10.1038/s41524-025-01868-z
  3. [3]N. Pugno, A. Carpinteri, M. Ippolito, A. Mattoni and L. Colombo. Atomistic fracture: QFM vs. MD. Engineering Fracture Mechanics 75 (2008) 1794–1803.doi: 10.1016/j.engfracmech.2007.01.028
  4. [4]S. Jaddi et al. Definitive engineering strength and fracture toughness of graphene through on-chip nanomechanics. Nature Communications 15 (2024) 5863.doi: 10.1038/s41467-024-49426-3
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